It is known in the prior art that an examination object can be disposed in the examination region of a medical imaging system, for example in the examination region of an x-ray system. A radiation source is moved around the examination object on an essentially planar, essentially circular scan path. A radiation detector is also moved around the examination object on an essentially planar, essentially circular scan path at the same time as the radiation source. The movements of the radiation source and radiation detector are linked in such a manner that the examination object (or the relevant part of the examination object) is constantly located between the radiation source and radiation detector. As the radiation source and radiation detector move, the radiation detector is used to capture two-dimensional projection images of the examination object. What is known as a filtered back-projection algorithm is used to determine a three-dimensional reconstruction of the examination object from the captured two-dimensional projection images. The Feldkamp algorithm in particular is generally known to those skilled in the art and is described for example in the technical paper [1].
For an expedient application of filtered back-projection algorithms the projection matrix of every two-dimensional projection image must be known, this being a matrix, which correctly describes the mapping of the three-dimensional space to the plane, in which the radiation detector is located on receipt of the respective projection image.
It is in theory conceivable to determine the parameters, which define the respective projection matrix, directly from the positioning and orientation of the radiation source and radiation detector and to define the projection matrix based on these parameters. In practice however this procedure proves to be too inaccurate—for example due to mechanical instabilities.
In practice a reference object is disposed in the examination region. Projection images of the reference object are captured from exactly the same positions of the radiation source and radiation detector, from which projection images of examination objects are to be captured later. With a suitable arrangement of the reference object it is possible to define the parameters, which define the projection matrix for the respective projection image, and therefore also the projection matrix itself from each projection image. This procedure is generally known to those skilled in the art and is described in more detail in the technical paper [7] for example.
For each projection image the projection matrices are related to a coordinate system, the location (in other words position and orientation) of which is defined in relation to the reference object. In order to be able to effect a three-dimensional reconstruction, the projection matrices of all the projection images used also have to relate to the same coordinate system. The reference object must therefore not only be disposed in the beam path or in the examination region, it also cannot be moved as the projection images are being captured.
The procedure described above for determining the projection matrices provides good results for standard filtered back-projection algorithms, which assume an essentially circular scan path.
In recent times reconstruction algorithms have become known, which are based on non-circular scan paths. The new types of scan paths consist for example of two circular paths intersecting each other orthogonally or one scan path consisting of a number of circular segments. Tests with simulated data show that these reconstruction algorithms have the potential to improve reconstruction accuracy. See also technical papers [2] to [6].
In principle the method for determining projection matrices described above can also be used for these reconstruction algorithms. In practice the problem however arises that standard reference objects were developed to determine the projection matrices for circular scan paths. Determining the projection matrices for positions of the radiation source and radiation detector, which do not lie on such a circular scan path, is however—depending on the location of the individual case—subject to greater inaccuracies, only possible to a limited degree and with difficulty or impossible.
It is of course possible to determine the projection matrices for the scan path to be traveled in segments, with the reference object being positioned correspondingly for every segment of the scan path. This means that the projected matrices are related to the same coordinate system within each segment of the scan path. It cannot however be ensured that the coordinate systems of different segments correspond. This is however essential when applying the reconstruction algorithms.
It is also conceivable that a reference object can be developed, with which it is possible to determine the projection matrices for all the projection images captured while traveling the respective scan path. However this is associated with a considerable development and financial outlay. Also it is currently not foreseeable whether such attempts will meet with the desired success.